Are you tired of using the traditional method of getting the square root of a number that involved six-digits or eight-digits numbers? Try this new exciting and challenging method of getting the square root of a special group of numbers in an easier way. Welcome to square edging!

Wednesday, August 25, 2010

S.E. "Grouping" Method

DEALING WITH SQUARES OF FIVE

Table of Multiples of Five Squares (M5.Sq)

052 = 0’25

152 = 2’25

252 = 6’25

352 = 12’25

452 = 20’25

552 = 30’25

652 = 42’25

752 = 56’25

852 = 72’25

952 = 90’25

If you look at the table above, you may notice that there are some “common things” about these following groups;

Group 1

152 = 2’25

352 = 12’25

652 = 42’25

852 = 72’25

Group 2

052 = 0’25 (sometimes, not included)

452 = 20’25

552 = 30’25

952 = 90’25

Group 3

252 = 6’25

752 = 56’25

Take Note:

1) The squares of 15, 35, 65 and 85, all end up with …225

2) The squares of 5, 45, 55 and 95, all end up with …025

3) The square of 25 and 75, end up with …6’25

Always remember that all squares of numbers having a last digit of 5, will all, end up with …25.

But the underlined numbers will give us a ‘hint’ of what the missing digits might be.

You will notice that the middle missing digit (N). could either be 1, 3, 6 or 8(The given problem belongs to Group 1 as indicated by the third to the last digit of √40’32’25).

Take note too, that the P-Chk also give us a hint that the ‘true square root’ is below 650 (Due to the notation 4↓),

Step 3

Underline the 1 and 3, indicating that 6 and 8 are eliminated:

P: 40’32

65: 42’25↓

4↓N : {0, 1, 2, 3, 4}

Step 4

Create A Square Root Locator

↓ 615 ..... 635 ↑

42’25 \

39’06 / ↑

36 .....

78’25 / 2

39’12

Therefore:

√ 403,225 = 635

MSM-2 seems to be simple when dealing with “squares of 5”in five or six digits. All you have to do is to determine which group the missing “middle-digit” belongs and slim down the possibility by using the P-Chk.

“SQUARES OF FIVE” IN EIGHT DIGITS

Case No. 1

Given Problem:

√ 21,949,225

Step 1:

Use the SE telegram procedure as initial instructions:

√ 21’94’92’25

.... 4 ........... 5

N : 1, 3, 6, 8

Step 2:

Create A P-Chk

P : 21’94

45: 20’25 ↑

5↑ M : 5, 6, 7, 8, 9

The N notation is telling us that ‘the second to the last digit’ of the possible square root (which is still unknown), could either ‘any’ of the indicated digits on its right side (Only one of them, 1, 3, 6 or 8 is the correct digit).

The M notation also tells us, that the second digit of the possible square roots could be either be 5, 6, 7, 8 or 9. So we have “4x5” combinations, starting with:

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I was inspired by the book of Stephen Hawking, “A Brief History of Time”, copyright 1988. From then on, I'd been obsessed (if that is the right word) to find out what gravity really is and based on this book, I made my own opinions about gravity in a non-conventional points of view.
I was also a Math Student before and creating Square Edging came from my own innovative thinking.
...as a repairman, I'm wishing to share my skill and experiences